We present a novel continuum robot design concept, Concentric Agonist-Antagonist Robots (CAAR), that uses push-pull, agonist-antagonist action of a pair of concentric tubes. The CAAR tubes are designed to have noncentral, offset neutral axes, and they are fixed together at their distal ends. Axial base translations then induce bending in the device. A CAAR segment can be created by selectively cutting asymmetric notches into the profile of two stock tubes, which relocates the neutral bending plane away from the center of the inner lumen. Like conventional concentric-tube robots (CTRs) based on counter-rotating precurved tubes, a CAAR can be made at very small scales and contain a large, open lumen. In contrast with CTRs, the CAAR concept has no elastic stability issues, offers a larger range of motion, and has lower overall stiffness. Furthermore, by varying the position of the neutral axes along the length of each tube, arbitrary, variable curvature actuation modes can be achieved. Precurving the tubes can additionally increase the workspace of a single segment. A single two-tube assembly can be used to create 3 degree-of-freedom (DOF) robot segments, and multiple segments can be deployed concentrically. Both additive manufacturing and traditional machining of stock tubes can create and customize the geometry and performance of the CAAR. In this paper, we explore the CAAR concept, provide kinematic and static models, and experimentally evaluate the model with a both a straight and a precurved CAAR. We conclude with a discussion of the significance and our plans for future work.